Modeling the growth of Pacific white shrimp (Litopenaeus vannamei) using the new Bayesian hierarchical approach based on correcting bias caused by incomplete or limited data

The revenue, costs, and profit of an aquaculture farm are based on the weight of animal protein sold. Thus, there is a relationship between the economic and zootechnical indexes to the growth model of animals in a production system. The growth modeling of cultivated organisms can be used as a production management tool, allowing estimates of anticipated size at harvest, waste outputs, as well as nutrient and feed requirements, helping in decision-making in the face of Aquaculture 4.0. It is important to emphasize that recent research has indicated the possible underestimation of parameters in nonlinear growth models due to the characteristic of incomplete or limited data in aquaculture. Therefore, the objective of this research was to model the growth of Pacific white shrimp (Litopenaeus vannamei) in an industrial-scale shrimp farm in northeastern Brazil. Based on the Bayesian methodology for correcting this bias, six nonlinear hierarchical growth models were evaluated in this research (Morgan-Mercer-Flodin, Michaelis-Menten, Weibull, von Bertalanffy, Gompertz, and logistic growth equation) and fitted to real data from a shrimp farm in northeastern Brazil. The model was validated based on the predictive capacity (accuracy) to forecasting shrimp growth at different hierarchical levels. Finally, for one of the main expected results, a sensitivity analysis was performed to compare different treatments according to the new approach. The Weibull growth equation stands out as the best among all those studied (WAIC = 2661.3, LOO-IC = 2705.2). Although it presented a poor fit for the hierarchical population level, good predictions were realized at the pond level and at the production cycle level. The dataset was split into fit and homologation subsets for a model validation analysis which showed an accuracy of 95.76% and 85.71% at the pond and production cycle levels respectively. The proposed method detected subtle differences between production cycles, which would be imperceptible if analyzed using the zootechnical indices usually practiced in shrimp farms. The new approach can contribute to improving products, processes, and decision-making in aquaculture management.

Automated summary

This study focused on modeling the growth of Pacific white shrimp in an industrial-scale shrimp farm in northeastern Brazil. Six nonlinear hierarchical growth models were evaluated and fitted to real data, with the Weibull growth equation showing the best performance in predicting shrimp growth. The proposed method detected subtle differences between production cycles and provided a new approach for improving products, processes, and decision-making in aquaculture management.